Sylow p-subgroup

If $(G,*)$ is a group then any subgroup of order $p^a$ for any integer a is called a p-subgroup. If $|G|=p^{a}m$, where $p\nmid m$ then any subgroup $S$ of $G$ with $|S|=p^a$ is a Sylow p-subgroup. We use ${\mathrm{Syl}}_{\mathrm{p}}(G)$ for the set of Sylow p-groups of $G$.

More generally, if $G$ is any group (not necessarily finite), a Sylow p-subgroup is a maximal $p$-subgroup of $G$.

Title	Sylow p-subgroup
Canonical name	SylowPsubgroup
Date of creation	2013-03-22 12:50:59
Last modified on	2013-03-22 12:50:59
Owner	Henry (455)
Last modified by	Henry (455)
Numerical id	8
Author	Henry (455)
Entry type	Definition
Classification	msc 20D20
Synonym	Sylow subgroup
Synonym	Sylow group
Related topic	SylowTheorems
Related topic	ProofOfSylowTheorems
Related topic	PPrimaryComponent
Related topic	SylowsThirdTheorem
Defines	Sylow p-subgroup
Defines	p-subgroup